bash-pure, 182 bytes

Result

WA

Code [DL]

#!bin/sh
for i in `seq 1 50`;do read j;k=`echo "ibase=2; $j"|bc`;for x in `seq 0 23`;do if [ $[$[$x*$[$x-1]]/2] -eq $k ];then echo 1;break;elif [ $x -eq 22 ];then echo 0;fi;done;done

stdin

00101101
01000101
01000110
00111010
11010010
00001000
01010110
01001110
11111001
01101011
00100100
00000000
00000001
00011110
11100111
00000011
10100111
00110111
11111101
10001000
10111110
11101111
00011100
00001010
01110000
01111000
11001000
01110111
11000100
00010101
00001111
10110110
10101111
10000100
01111010
10001001
01011011
10101011
01001110
10011011
10101110
00000110
00001011
11011001
10100011
10011001
01000010
10100110
10001000
01101001

stdout

stderr

/bin/bash: warning: setlocale: LC_ALL: cannot change locale (en_US.UTF-8)
/code.bash: line 2: seq: command not found

strace